Bioeconomic modeling for control of weeds in natural environments

When a weed invasion is first discovered a decision has to be made on whether to attempt to eradicate it, contain it or do nothing. Ideally, these decisions should be based on a complete benefit-cost analysis, but this is often not possible. A partial analysis, combining knowledge of the rate of spread, seedbank longevity, costs of control and techniques of economic analysis, can assist in making a good decision. This paper presents a decision model to determine when immediate eradication of a weed should be attempted, or more generally whether weed control should be attempted at all. The technique is based on identifying two ‘switching points’: the invasion size at which it is no longer optimal to attempt eradication but where containment may be an option; and the invasion size at which it becomes optimal to apply no form of control at all. The model is applied to a woody perennial weed in a natural environment. The results show that seedbank longevity is the main constraint on the maximum eradicable area and spread rate is the main constraint on the maximum containment area. Stochastic simulations are undertaken to derive probability distributions of costs which are than used to evaluate the effect of budget constraints on areas that can be eradicated. We find that, in the absence of a budget constraint, it may be desirable to eradicate invasions from areas as large as 8000 ha, but when budget constraints typical of those faced by agencies in Australia are introduced, feasible eradicable areas are less than 1000 ha.     

Managing Systems with Non-convex Positive Feedback

We study here optimal management of dynamic ecological systemsthat exhibit a destabilizing positive feedback. The prototypeexample is that of a shallow lake in which phosphorous loadingplaced by anthropogenic activities (fertilizers for farmingand gardening) is stored in sediments until a critical levelis reached after which there is a destabilizing return to thewater – the tradeoff between farming interests and lake qualitygenerates an optimal control problem. We show that in such systems, there may be a variety of local optima and associatedbasins of attraction wherein the optimal path may depend onstarting state (phosphorous stock). We characterize the variouspossible optimal behaviors and identify the ambiguities thatcan only be resolved by choice of functional form.     

Optimal dynamic scale and structure of a multi-pollution economy

We analyze the optimal dynamic scale and structure of a two-sector-economy, where each sector produces one consumption good and one specific pollutant. Both pollutants accumulate at different rates to stocks which damage the natural environment. This acts as a dynamic driving force for the economy. Our analysis shows that along the optimal time path (i) the time scale of economic dynamics is mainly determined by the lifetime of pollutants, their instantaneous harmfulness and the discount rate; (ii) economic scale and structure, as well as resulting welfare, may be non-monotonic, and (iii) environmental damage may exhibit an inverted U-shape form. These results raise important questions about the optimal design of environmental policies in a multi-pollution economy. We suggest a system of dynamic Pigouvian emission taxes, each of which should be levied specifically on one particular pollutant. We show that the optimal time path of each tax level is determined by the characteristics not only of that particular pollutant but also of all other pollutants.     

A bioeconomic model for determining the optimal response strategies for a new weed incursion

Invasions by non-indigenous plant species pose serious economic threats to Australian agricultural industries. When a new invader is identified a rapid response is critical, particularly if the invasive species has the ability to spread rapidly. An early decision is required whether to attempt to eradicate or contain the infestation, or do nothing and leave it to landholders to manage. These decisions should be based on economic considerations that account for long term benefits and costs. This paper describes a bioeconomic simulation framework with a mathematical model representing weed spread linked to a dynamic programming model to provide a means of determining the economically optimal weed management strategies over time, from the government’s perspective. The modelling framework is used to evaluate hypothetical case study invasive weed control scenarios in the Australian cropping systems. The benefit–cost ratios of invasion control are shown to be generally very high and clearly, there are significant benefits to be achieved by controlling highly invasive weeds when initial infestations are at a low level. Even if the invasion cannot be eradicated due to its high invasiveness or budget constraints, it still pays to maintain invasions at low levels.     

An optimization framework for addressing aquatic invasive species

This study develops a bio-economic model framework to optimize the management of aquatic invasive species. Stochastic dynamic programming is applied to investigate when and to what extent a society should engage in efforts to reduce the likelihood of an invasion, to control and eradicate a newly established population, and to adapt to damages. The framework is parameterized for a potential Asian clam (Corbicula fluminea) invasion in the warm water discharge area of a nuclear power plant planned on the northern shores of the Baltic Sea. The sensitivity analysis reveals three distinct strategies: an adaptive strategy, which reduces the damage that an existing invasive species population causes to the private sector; a preventive strategy, which delays the invasion and the resulting damage; and a mitigative strategy, which puts effort into timely detection, control and eradication of the newly established population. Choice of the optimal strategy is sensitive to the unit costs and effectiveness of the measures required, to the level of externalities and to the size of the clam population after the invasion has been detected. The results emphasize the need for the energy sector to identify and internalize the external costs of potential invasions when making any large-scale investment plans.     

Public budget composition,fiscal (de)centralization,and welfare

Abstract We study the optimal degree of fiscal decentralization in a dynamic federal economy where governments decide on budget size and its allocation between public education and infrastructure spending. We find that full centralization of tax and expenditure policies is optimal when infrastructure productivity is similar across regions. When differences are not too large, partial centralization is optimal. With strong differences, full decentralization becomes optimal. National steady‐state output tends to be highest under full decentralization. We provide a justification for the mixed evidence regarding the Oates conjecture by showing that full dominates partial decentralization, despite being inferior to complete decentralization.     

Optimal contracting with dynastic altruism: Family size and per capita consumption

We use a Barro–Becker model of endogenous fertility, in which parents are subject to idiosyncratic shocks that are private information (either to labor productivity or taste for leisure), to study the efficient degree of consumption inequality in the long run. The planner uses the trade-off between family size and future consumption and leisure, to provide incentives for workers to reveal their shocks. We show that in this environment, the optimal dynamic contract no longer features immiseration in consumption. We also discuss the implications of the model on the long run properties of family size in the optimal contract and show that the long run trend in dynasty size can be either positive or negative depending on parameters.     

Fishing in a Shallow Lake: Exploring a Classic Fishery Model in a Habitat with Shallow Lake Dynamics

Renewable resources such as fish exist within habitats. Harvesting activities may directly impact the habitat, beyond the influence caused by changing the balance between species. When harvesting activities impact stock size and habitat health in different ways, both states must be explicitly considered. A classic fisheries model is embedded in a habitat that exhibits shallow lake dynamics, where carrying capacity depends on habitat health and fishing effort damages the habitat. Hysteresis in the habitat dynamics can manifest itself as multiple steady states for both the dynamic and open access solutions. Numerical explorations of the model suggest that a new fishery in such a setting should often be managed to protect the health of the habitat, while it may not be optimal to restore a fishery in an already degraded habitat. Conventional policy tools applied in their classic form are unlikely to be effective.     

Designing social security - a portfolio choice approach

Public social security systems may provide diversification of risks to individuals’ life-time income. Capturing that a pay-as-you-go system (paygo) may be considered as a “quasi-asset”, we study the optimal size of the paygo system as well as the optimal split between funded and unfunded pension saving by means of a theoretical portfolio choice framework. A low-yielding paygo system can benefit individuals if it contributes to hedge other risks to their lifetime resources. Numerical calculations indicate that optimal social security systems should be at least partly paygo financed in many economies. The optimal magnitude of the paygo system depends on the specified risk concept as well as the stochastic properties of stock market returns and implicit paygo-returns.     

Control and the management of a spreading invader

We consider the problem of management of an aquatic invader spreading in a lake system. We assume that each year the invader can be removed from a certain proportion of invaded lakes, which depends on the selected intensity of control. Control decisions are generated and compared for an optimally controlled system and for a static optimization across asymptotic steady states. Control close to eradication of the invasive species is always optimal for invasions with relatively high damages, low rates of density dependent spread and/or low chance of additional random introductions. Control to a highly invaded steady state is optimal for those invasions with low relative damages, high chances of random introduction and high levels of uncertainty in species location. In all other cases the optimal outcome depends upon initial conditions. Comparing the relative performance of the optimally controlled system and the static optimization demonstrates situations when the differences are small and when not. When invasions are acted upon in their later stages and across certain parameter combinations a static optimization provides a reasonable approximation of an optimally controlled system. The flip-side is that optimal policies directed at an invasion in its early stages tend to provide significantly savings. The savings vary across parameter combinations, yet in these situations little useful insight will be generated without consideration of a dynamically optimized system.     

The value of (bounded) memory in a changing world

This paper explores the value of memory in decision making in dynamic environments. We examine the decision problem faced by an agent with bounded memory who receives a sequence of signals from a partially observable Markov decision process. We characterize environments in which the optimal memory consists of only two states. In addition, we show that the marginal value of additional memory states need not be positive and may even be negative in the absence of free disposal.     

FOR‐PROFIT SEARCH PLATFORMS

We consider optimal pricing by a profit‐maximizing platform running a dynamic search and matching market. Buyers and sellers enter in cohorts over time, meet, and bargain under private information. The optimal centralized mechanism, which involves posting a bid–ask spread, can be decentralized through participation fees charged by the intermediary to both sides. The sum of buyers' and sellers' fees equals the sum of inverse hazard rates of the marginal types, and their ratio equals the ratio of buyers' and sellers' bargaining weights. We also show that a monopolistic intermediary in a search market may be welfare enhancing.     

Importing exotic plants and the risk of invasion: are market-based instruments adequate?

Exotic plant species are often intentionally imported into regions outside of their normal range as ornamental plants or as breeding stock, thereby generating benefits for consumers and producers. However, one of the unintended side effects of such introductions is that the exotic plant species may become invasive. Prohibiting sale of this type of exotic plant species, on the basis that it may become invasive, will have social costs in the form of foregone consumer benefits and nursery profits. We develop a model of a private commercial plant breeding industry that imports an exotic plant species into a region. The risk associated with invasion is modeled using a probabilistic ‘hazard function’, the key determinants of which are the characteristics of the exotic plant and the number of commercial nurseries contributing to its dispersal. We consider the possibility of employing market-based instruments (e.g., Pigovian tax) consistent with the concept of ‘introducers pay’, to regulate the nursery industry. We then provide an empirical illustration using the historical introduction of saltcedar (Tamarisk spp.) into the United States. Our results indicate that the mere presence of a risk of invasion does not mean that it is socially optimal to prevent commercial sales of an exotic plant species. Indeed, there appear to be plausible forms of the functional relationships involved that require only a modest reduction in the private industry optimum. In contrast, no sales of the exotic plant should occur at all under several sets of assumptions about the level of invasion risk and the linkage between dispersal sites and invasion hazard.     

Take a risk: Preferring prevention over control of biological invaders

Scientists have argued that invasive species can be managed most cost effectively with greater investments in prevention. Further, under ideas like the precautionary principle it is reasonable to expect that a cautious manager would use more prevention relative to control because it keeps more invaders out. Yet, this is not typically done. In many cases, private and public resources are invested primarily to control existing invaders rather than to prevent new invasions. Managers frequently wait until after invaders have arrived and then scramble to limit the damages. We believe these paradoxical decisions can be understood by recognizing the link between typical human preferences for risk bearing and the technology of risk reduction. We demonstrate quantitatively how managers perceived to be cautious or averse to risk tend to shy away from prevention relative to control. This counterintuitive result arises because control is a safer choice than prevention because its productivity is relatively less risky: it works to remove existing invaders from the system. In contrast, the productivity of prevention is more uncertain because prevention only reduces the chance of invasion, it does not eliminate it, and invasion may not occur even in the absence of prevention. Managers' averse to risk will inherently avoid as much uncertainty as possible, whether the source of uncertainty regards ecological outcomes or economic productivity. Implications for environmental decision making are clear. In invasive species management, if managers act as though they are risk averse, their caution can backfire when it leads to more control rather than prevention. The social consequences of this choice are a greater probability of future invasions and lower social welfare. Our results suggest that social welfare is highest when managers were willing to “take a risk” with prevention.     

Quality competition and entry: a media market case

In this paper, we study the optimal tax policy in a differential oligopoly game where the competing firms share the access to a productive renewable resource. We show that, in a Feedback Nash Equilibrium of the game, a linear Markov tax, imposed on the output, and specified as an affine function of the available resource stock, leads the competing firms to produce the socially optimal quantities over time, thus overcoming the dynamic interplay between the tragedy of the commons and the firms’ market power. The optimal tax turns out to be independent from the resource stock in a monopoly, and it cannot be defined in a duopoly.     

Closed-loop equilibrium in a multi-stage innovation race

Summary. We examine a multistage model of an R&D race where players have multiple projects. We also develop perturbation methods for general dynamic games that can be expressed as analytic operators in a Banach space. We apply these perturbation methods to solve races with a small prize. We compute second-order asymptotically valid solutions for equilibrium and socially optimal decisions to determine qualitative properties of equilibrium. We find that innovators invest relatively too much on risky projects. Strategic reactions are ambiguous in general; in particular, a player may increase expenditures as his opponent moves ahead of him. Received: January 3, 2002; revised version: June 14, 2002 RID="*" ID="*" This is the final version of Judd (1985). The author gratefully acknowledges the comments of anonymous referees, Paul Milgrom, seminar participants at Northwestern University, the University of Chicago, the 1984 Summer Meetings of the Econometric Society, University of California at Berkeley, Stanford University, and Yale University, and the financial support of the National Science Foundation (SES-8409786, SES-8606581)     

Optimal age‐dependent income taxation in a dynamic extensive model: The case for negative participation tax on young people

We consider optimal age‐dependent income taxation in a dynamic model where the labor‐leisure choice is the extensive margin, each household faces idiosyncratic shocks to labor productivity and a pecuniary cost to work, and there is no insurance market against the shocks. We show that the well‐known property of the optimal participation tax rate in the static model continues to hold in our dynamic economy, that is, the participation tax rates for some income groups with low consumption are likely negative. In dynamic models, the optimal participation tax rate depends on age and on labor income. Our numerical simulations suggest that a negative participation tax should be restricted to young households.     

SOME WELFARE IMPLICATIONS OF OPTIMAL STABILISATION POLICY IN AN ECONOMY WITH CAPITAL AND STICKY PRICES

In this paper we review and extend some of the key lessons that seem to be emerging from the Ramsey‐inspired theory of dynamic optimal monetary and fiscal policies. We construct measures of the key distortions in our economy; we label these ‘dynamic wedges’. Inflation, actual or anticipated, distorts these wedges in the present period, shrinks the tax base and increases the deadweight loss. We show that, if possible, labour as well as capital ought to be subsidised in steady state. We point to a number of extensions to the Ramsey literature that may help in the formulation of actual policy.     

Optimal Dynamic Control of Visitors and Endangered Species in a National Park

To enable visitors to enjoy nature while protecting endangered species is the key challenge for national parks around the world. In our optimal dynamic control model, a park management maximizes tourism revenues and conservation benefits net of control costs by choosing optimal dynamic levels of conservation and visitor management. The optimization is constrained by an extended food chain model representing species-habitat-visitor interactions. We illustrate for a game bird in an Alpine national park that ecotourism can indeed lead to ecosystem degradation when the park management is more concerned about increasing tourism revenues than about achieving the conservation target and if the endangered species is unknown to most visitors. If, however, the park management is well aware of the potentially negative consequences of ecotourism and hence cares for species conservation, limited ecotourism can provide funding for species conservation which ensures population levels above the uncontrolled steady state.     

Commercialization of a demand-enhancing innovation: The release of a new apple variety by a public university

The upsurge of patented fruit varieties developed by university plant-breeding programs motivated this re-examination of optimal commercialization strategies when an innovator cares about profits for both itself and the licensees. Our theoretical findings suggest that the optimal licensing arrangement that maximizes weighted joint profits depends on the innovation level size, number of firms, and the weights assigned to the innovator and licensee profits. We designed an experiment to test the case with a small number of firms and found that the joint profits are the greatest under an exclusive per-unit royalty scheme. However, when the number of firms is large, as may be the case for a varietal introduction into the U.S. apple industry, our model suggests that the joint profits will be the largest under a nonexclusive contract, either with a two-part tariff, if the innovation level is high, or a per-unit royalty if the innovation level is low.